arXiv:2606. 14954v1 Announce Type: cross Abstract: We develop a general framework for analyzing representation costs of parametric data-fitting methods through their parameter-space regularizers.
arXiv:2607. 02003v1 Announce Type: cross Abstract: Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochastic heuristics.
arXiv:2509. 26371v3 Announce Type: replace-cross Abstract: Recently, there has been growing interest in characterizing the function spaces underlying neural networks.
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.
arXiv:2606. 01244v2 Announce Type: replace-cross Abstract: Inspired by the function-space theory of neural networks, we formulate and analyze a variation space for nonlinear operators between Hilbert spaces, defined through vector-valued Borel measures of bounded variation.
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
arXiv:2106. 04770v2 Announce Type: replace Abstract: We study parameter nonuniqueness in continuous-width depth-two fully connected neural networks.
The paper investigates how the choice of the π parameter in λπ norm-constrained adversarial attacks influences the sparsity and smoothness of the perturbations. By applying two established sparsity metrics and introducing three new smoothness measures—including one based on first-order Taylor approximations—the authors perform extensive experiments on real-world image datasets and various neural network architectures. Their results indicate that λρ norms with π values between 1.3 and 1.5 consistently provide the best balance between sparsity and smoothness, challenging the common use of λ1 or λ2 norms.
The paper studies operator learning on function spaces using encoder–decoder architectures. It shows that as input and output resolutions grow, the induced kernels converge to a limiting kernel, enabling regularity assumptions independent of resolution. The authors derive upper and lower bounds for regularized stochastic gradient descent, extend the analysis to neural networks via the limiting neural tangent kernel, and provide error bounds and complexity guarantees for various kernel and encoding constructions.
arXiv:2609.38049v1 Announce Type: new Abstract: Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite...
Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FF...
We develop a comprehensive theory for regularized M-estimation in reproducing kernel Hilbert spaces. Under mild conditions on the loss we establish existence and measurability of the estimator, covering a wide range of convex and non-convex losses, including bounded robust losses.